Today I encountered a downtime in my server ,the reason was not clear. after that i disabled the PHP suEXEC daemon mode and did not get any 503 fix mail ,
3 hours later I encountered the sites is not loading problem , after checking server from cpanel I saw my server load is too high (near 200 and every second goes up) , login to ssh was not possible also i can't kill any process from cpanel process manager , i performed a hardware reboot and after that i set LVE to off and switch back to 4.1.13 , now after 7h i did not see any problem .

It looks like CloudLinux resource limit was hit, and causes 503 errors in your case.
You should be careful with "PHP suEXEC max conn", if set it too high, while CageFS/LVE limit was not high enough, it will cause trouble during traffic surge.